Let the Wyatt's go through the face roster for next 2-3 months. Wyatt then cuts a promo on how they're the most dominant force in Wrestling and no one can stop them. Cue The Shield, who'd get a face pop, setting up The Shield Vs. The Wyatts at Survivor Series with The Shield belts on the line.

They could have the Wyatt Family ganging up on some random victim, and out of nowhere The Shield's music hits in the middle of it and they come walking down to the ring. They surround the family and a fight breaks loose, with Bray Wyatt running off before anyone from The Shield can get their hands on him.

The Shield can bring up the injustice in the Wyatt's attacks and remind them that there's another powerful group in the WWE. The Shield says they should pick on guys where the odds are even. The match is set for Mania and we get tons of great Ambrose/Wyatt promos on the buildup to the biggest show of the year.

But if they continue to shove the Shield promos to the APP or the website, it is ruined.

Lets make it simple. Have The Shield interrupt one of Wyatt's rants, and of course after they have just destroyed some unlucky mid card talent. Have the Wyatt Family go over The Shield, and eventually break the trio apart. Thus, showing how powerful Bray is at mind games. The Shield have had their run, it's time to end it.

Just because they're both stables of 3 people doesn't mean they have to feud. That's the same as saying two wrestlers should team up just because they're black.

That's true, but I don't think it's the fact that they're both a group of 3 guys that makes this match so intriguing for the people that bring it up. If that were the case, you'd probably see more requests to build up 3MB and get them involved in a similar feud/match. Both are "dark" stables, and each have one amazing mic worker with very unique styles (Ambrose/Wyatt). Both groups have created a lot of buzz and seem to have promising futures, so it's merely a great opportunity to put them against each other before one of them splits.

I'd be ok with an Ambrose/Reigns/Rollins triple threat at Wrestlemania instead, but Shield vs. Wyatt Family is hard to pass up for me as well.

while stable wars are cool and all, this one would just make no sense.

Sure it would, you'd have to build the Wyatt Family up for awhile to make them seem like a legitimate force, and then after that have The Shield step in and say they're tired of somebody else coming in and trying to take over their territory, their "yard" as a certain color commentator would say. It literally almost writes itself, plus The Shield would make perfect defenders, for lack of a better word, of the WWE from the Wyatt threat.